Pan-Seared Strip Steak with Red-Wine Pan Sauce and Pink-Peppercorn Butter
['1/4 cup (1/2 stick) unsalted butter, room temperature', '1 teaspoon minced fresh thyme', '1 teaspoon honey', '1 teaspoon whole pink peppercorns', 'Coarse kosher salt', '1 10-ounce New York strip steak (about 1 1/4 to 1 1/2 inches thick)', '2 teaspoons extra-virgin olive oil, divided', '1 teaspoon minced fresh thyme', 'Coarse kosher salt', '1/4 cup thinly sliced shallot', '1 cup dry red wine', '1/2 cup low-salt beef broth or low-salt chicken broth', 'Celery Root and Parsnip Puree']
Combine first 4 ingredients in small bowl; mix with fork until peppercorns are slightly crushed.
Season with coarse salt and black pepper. Place small sheet of plastic wrap on work surface; place butter mixture atop plastic. Using plastic wrap as aid, form butter mixture into 1 1⁄2-inch-diameter cylinder; wrap tightly and chill. DO AHEAD: Can be made 3 days ahead. Keep chilled. Bring to room temperature before using.
Rub steak with 1 teaspoon oil; sprinkle both sides with thyme, then coarse salt and 1/4 teaspoon black pepper. Let steak stand at room temperature 30 minutes.
Heat medium nonstick skillet over medium-high heat. Add steak; cook to desired doneness, 3 to 4 minutes per side for medium-rare. Transfer steak to plate; tent with foil. Add 1 teaspoon oil to skillet; add shallot and sauté until slightly softened, scraping up browned bits. Add wine; boil until liquid is reduced by half, stirring often, about 1 minute. Add broth; boil until sauce is thickened, about 2 minutes. Whisk in 3 tablespoons pink-peppercorn butter. Season sauce with coarse salt and pepper.
Cut steak against grain into 1/3-inch- thick slices. Divide between plates. Top with sauce; serve with puree.
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